Chapter 5. Fluidization Chapter 5. Fluidization 5.1 Fundamental * ®â€‌p vs. U...

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Transcript of Chapter 5. Fluidization Chapter 5. Fluidization 5.1 Fundamental * ®â€‌p vs. U...

  • Chapter 5. Fluidization

    5.1 Fundamental

    * Δ p vs. U Figure 5.1

    Minimum (incipient) fluidization, U mf

    From force balance

    Net downward force

    Δp= ( 1- ε )( ρ p- ρ g )H (1)

    Net upward force

    Δp H

    = 150 ( 1- ε ) 2

    ε 3 μU

    x 2sv + 1.75

    1- ε

    ε 3 ρ gU

    2

    x sv (2)

    Equating (1) and (2) at U=U mf

    Ar=150 ( 1- ε ) ε 3

    Re mf+1.75 1 ε 3 Re

    2 mf

    where Ar≡ ρ gx

    3 sv (ρ p- ρ f)g

    μ 2 , Archimedes number

    Re mf= ρ fU mfx sv μ

    ε= 0.4, usually

    More practically,

    Wen and Yu(1966) for x sv > 1 0 0 μm

    Ar= 1056Remf+159Re 2 mf

    Baeyens and Geldart(1974) for x < 1 0 0 μ m

    U mf= ( ρ p- ρ f)

    0.934g 0.934x 1.8

    1110μ 0.87ρ 0.066f

    5.2 Relevant Powder and Particle Properties

  • - Absolute density: materials property

    - Particle density: Figure 5.2

    - Bed density

    * Sieve diameter, x p , x v= 1.13x p

    mean x p= 1

    ∑m i/x i

    5.3 Bubbling and Non-Bubbling Fluidization

    Types of Fluidization

    Various types of fluidized beds

    - Bubbling fluidized bed : Figure 5.3 for Group B particles

  • - Liquid fluidization: Figure 5.4

    5.4 Classification of Powders

    Geldart(1974) Figure 5.6

    Table 5.1

    Group A : Nonbubbling for U m f < U < U m b

    where

    U mb= 2.07 exp (0.716F ) [ xρ 0.06g μ 0.347 ]

    where F : fraction of powder less than 45 μm

    Bubbling for U > U m b

    Maximum bubble size

    d Bv, max = 2 g

    (U T2.7 ) 2

    Group B : Bubbling for U > U m f

    No maximum in bubble size

    Slugging ( d B≥ 1 3 D) - Figure 5.8 (right)

    Tagi and Muchi (1952)

    In order to avoid slug formation

    ( H m f D )≤

    1.9

    ( ρ p x p ) 0.3

    Slug forms when ( H m f D ) >

    1 . 9

    ( ρ p x p ) 0 . 3

    and

    U > U mf+0.16(1.3 4D 0.175-H mf)

    2+ 0.07( gD ) 1/2

    Group D : Spoutable

  • Group C : Subject to channeling in large diameter-bed

    5.5 Expansion of a Fluidized Bed

    (1) Nonbubbling Fluidized Bed

    Upward superficial fluid velocity(or volumetric flux)

    U= U Tε 2f(ε) =U T ε

    n

    For Re p≤0.3, n= 4.65

    For Re p≥500, n= 2.4

    Assuming conservation of bed mass, M B

    M B= (1- ε )ρ pAH

    ∴ ( 1- ε 1 )ρ pAH 1 = ( 1- ε 2 )ρ pAH 2

    ∴ H 2 H 1

    = 1- ε 1 1- ε 2

    Worked Example 5.1

    (2) Bubbling Fluidized Bed

    The bed is assumed to consist of two phases:

    - Dense (particulate, emulsion) phase : a state of minimum

    fluidization

    - Lean (bubble) phase : flow of gas in excess of minimum

    fluidization as bubbles

    Gas flow as bubbles= Q-Qmf= (U-Umf )A

    Gas flow in the emulsion phase=Qmf=UmfA

    ε B=

    H-Hmf H

    = QB AU B

    = U-Umf U B

    * Mean bed voidage, 1- ε= ( 1- ε B )( 1- ε mf)

    * Bubble Size and Rise Velocity

    U B= Φ B (gd Bv ) 1/2

    where Φ B= function of D

  • For group B

    d Bv= 0.54

    g 0.2 (U-U mf )

    0.4(L+4N - 1/2 ) 0.8

    where N : the number of holes/m 2

    L : distance above the distributor

    5.6 Entrainment

    - Carryover, elutriation

    Zone above fluidized bed (Freeboard) - Figure 5.11

    - Splash zone

    - Transport disengagement zone

    Transport disengagement height,

    TDH from Figure 5.12 or

    TDH= 4.47d 0.5Bvs

    - Dilute-phase transport zone

    Worked Example 5.1

    Instantaneous entrainment rate of size x i

    R i=- d dt

    (MBmBi)=K * ihAm Bi

    where M B: total mass of solids in the bed

    A: area of bed surface

    m Bi: fraction of bed mass with size x i at time t

    K *ih: elutriation constant

    Total rate of entrainment

    R T=- d dt

    [∑(MBm Bi)]=∑K * ihAm Bi

    K * i∞ : K *ih above TDH - (5.45) and (5.46)

    Worked Example 5.2

  • 5.7 Heat transfer in Fluidized Bed

    Heat transfer between particles and gas

    Nu= 0.03Re 1.3p ( Re p≺50)

    where Nu= h gpx

    k g

    L 0.5 : L for T g-T s T g0-T s

    =0.5

    Very short(0.95mm~5mm)

    Heat transfer between surface and bed

    h = h p c + h g c + h r

    particle gas radiation convection convection

    Figure 5.14: h pc is controlled by k g

    Figure 5.15: maximum occurs by blanket of bubbles

    When U > ( 2 ∼ 3 )×U m f

    For group B powders

    h max = 35.8k 0.6 g

    ρ 0.2 p

    x 0.36

    , W/m2K

    For group A powders

    Nu max = 0.157Ar 0.475

    5.8 Applications of Fluidized Beds

    Advantages

    - Liquid-like behavior, easy to control and automate

    - Rapid mixing, uniform temperature and concentration

    - Resists rapid temperature changes, hence responds slowly to

    changes in operating conditions and avoids temperature runaway

  • with exothermic reactions

    - Circulate solids between fluidized beds for heat exchange

    - Applicable for large or small scale operations

    - Heat and mass transfer rates are high, requiring smaller

    surfaces

    Disadvantages

    - Bubbling beds are difficult to predict and are less efficient

    - Rapid mixing of solids causes nonuniform residence times for

    continuous flow reactors

    - Particle comminution(breakup) is common

    - Pipe and vessel walls erode to collisions by particles

    (1) Physical Processes

    Drying / Mixing / Granulation / Coating / Heat exchanger/

    Adsorption(Desorption)

    Figure 5.17

    (2) Chemical Processes

    Table 5.2

    Figure 5.18 Fluidized catalytic cracker

    5.9 A Simple Model for the Bubbling Fluidized Bed

    Reactor

    Figure 5.19

    Orcutt et al(1962)

    Form the overall mass balance on the reactant + shell mass balance

    1- C H C 0

    = (1- βe - χ )-

    ( 1- βe - χ ) 2

    kH mf( 1- ε p )

    U + (1- β e -

    χ )

  • C BH= C P+ (C 0-C P) exp [- χ ]

    C P= C 0[U-(U-U mf )e

    - χ]

    kH mf(1- ε P )+ [U (U-U mf)e - χ]

    CH= UmfC P+(U-Umf)CBH

    U

    where C 0 : concentration of reactant at distributor

    C H : concentration of reactant leaving the reactor(H)

    C B : concentration of the reactant in the bubble phase

    C P : concentration of the reactant in the particulate phase

    β= U-Umf U

    and χ= K cH

    U B

    where K c: mass transfer coefficient of the reactant from particulate

    phase

    Figure 5.20

    Worked Example 5.3